Methods, Systems, and Computer-readable Media for Reference Impedance Adaptation in Electromagnetic Simulation and Modeling

ABSTRACT

Methods, systems, and computer-readable media for reference impedance adaptation are disclosed. The method may comprise a step of providing a network model of a circuit having at least one port, wherein the network model includes at least one network parameter, the network parameter being associated with the port and being defined based on a reference impedance of the port. The method may further comprise computing an input impedance of the port based on the network parameter. The method may also include defining a new reference impedance for the port based on the input impedance. Moreover, the method may include calculating a new network parameter of the network model based on the new reference impedance.

TECHNICAL FIELD

The present invention relates to methods, systems, and computer-readablemedia for simulating and modeling electrical components, interconnects,and microwave/RF circuits. More particularly, the present inventionrelates to methods, systems, and computer-readable media for adaptivelychanging reference impedance of network in calculating networkparameters, such as S-parameters.

BACKGROUND

In electromagnetic simulation and analysis, network models are oftenutilized for analyzing electrical components, circuits, and systems.Network models may be characterized by network parameters, such asimpedance parameters and scattering parameters (S-parameters).

S-parameters are often represented in matrix form and associated withreference impedance. The reference impedance is often set to be 50 Ohms(Ω), partly because the characteristic impedance of typical signaltransmission line systems is around 50 Ω. However, for systems withpower/ground lines, the effective input impedance is typically muchsmaller than 50 Ω. Therefore, S-parameters generated using 50 Ωreference impedance may be insensitive to the variation of electricalproperties of power/ground systems.

Accordingly, there is a need for a system and method for adaptingreference impedance in order to improve accuracy in electromagneticsimulation and modeling.

SUMMARY

Some aspects of the disclosed embodiments may involve methods, systems,and computer-readable media for analyzing electrical properties of acircuit. The method may comprise a step of providing a network model ofthe circuit having at least one port, wherein the network model includesat least one network parameter, the network parameter being associatedwith the port and being defined based on a reference impedance of theport. The method may further comprise computing an input impedance ofthe port based on the network parameter. The method may also includedefining a new reference impedance for the port based on the inputimpedance. Moreover, the method may include calculating a new networkparameter of the network model based on the new reference impedance.

The preceding summary is not intended to restrict in any way the scopeof the claimed invention. In addition, it is to be understood that boththe foregoing general description and the following detailed descriptionare exemplary and explanatory only and are not restrictive of theinvention, as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate various embodiments and exemplaryaspects of the present invention and, together with the description,explain principles of the invention. In the drawings:

FIG. 1 shows an exemplary system for simulating and/or analyzing anelectrical circuit, consistent with some disclosed embodiments;

FIGS. 2A and 2B are schematic diagrams of a network model, in accordancewith some disclosed embodiments;

FIGS. 3A and 3B illustrate an exemplary method for impedance adaptationfor a one-port network, in accordance with some disclosed embodiments;

FIGS. 4A and 4B illustrate an exemplary method for impedance adaptationfor a multi-port network, in accordance with some disclosed embodiments;

FIG. 5A-5C are flow charts of exemplary methods for impedanceadaptation, in accordance with some disclosed embodiments;

FIG. 6 is a flow chart of an exemplary method of modeling electricalcircuit using new network parameters resulting from impedanceadaptation, in accordance with some disclosed embodiments; and

FIG. 7 shows an exemplary graph comparing S-parameter variations beforeand after performing reference impedance adaptation, in accordance withsome disclosed embodiments.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

Reference will now be made in detail to exemplary embodiments of theinvention, examples of which are illustrated in the accompanyingdrawings. When appropriate, the same reference numbers are usedthroughout the drawings to refer to the same or like parts.

Embodiments of the present disclosure may involve system, method, andcomputer-readable medium for simulating and/or analyzing an electricalcircuit. The term “electrical circuit” (or “circuit”) may refer to anypath which electrons from a voltage or current source follow. Electricalcircuits may be physically implemented on circuit structures such asintegrated circuit (IC) chips, modules, chip or module carriers, cards,boards, and/or back-planes. Such circuit structures may include multiplelayers to sandwich electronic components and/or signal/power/groundlines. During design, fabrication, and/or testing of electricalcircuits, computer simulation may be performed to analyze, evaluate,and/or verify electrical properties and/or behaviors of the circuits.

FIG. 1 shows an exemplary system 100 for simulating an electricalcircuit. Consistent with some embodiments, system 100 may be a generalpurpose computer, or a computing device dedicated for simulation. Asshown in FIG. 1, system 100 may include a processor 110, a memory module120, a user input device 130, a display device 140, and a communicationinterface 150. Processor 110 can be a central processing unit (“CPU”) ora graphic processing unit (“GPU”). Depending on the type of hardwarebeing used, processor 110 can include one or more printed circuitboards, and/or a microprocessor chip. Processor 110 can executesequences of computer program instructions to perform various methodsthat will be explained in greater detail below.

Memory module 120 can include, among other things, a random accessmemory (“RAM”) and a read-only memory (“ROM”). The computer programinstructions can be accessed and read from the ROM, or any othersuitable memory location, and loaded into the RAM for execution byprocessor 110. For example, memory module 120 may store one or moresoftware applications. Software applications stored in memory module 120may comprise operating system 122 for common computer systems as well asfor software-controlled devices. Further, memory module may store anentire software application or only a part of a software applicationthat is executable by processor 110.

In some embodiments, memory module 120 may store simulation software 124that may be executed by processor 110. For example, simulation software124 may be executed to simulate electrical behaviors/properties ofelectrical circuits. It is also contemplated that simulation software124 or portions of it may be stored on a removable computer readablemedium, such as a hard drive, computer disk, CD-ROM, DVD±R, CD+RW orDVD+RW, HD or Blu-ray DVD, USB flash drive, SD card, memory stick, orany other suitable medium, and may run on any suitable component ofsystem 100. For example, portions of applications to perform simulationmay reside on a removable computer readable medium and be read and actedupon by processor 110 using routines that have been copied to memory120.

In some embodiments, memory module 120 may also store master data, userdata, application data and/or program code. For example, memory module120 may store a database 126 having therein various simulation data usedfor simulating electrical circuits.

In some embodiments, input device 130 and display device 140 may becoupled to processor 110 through appropriate interfacing circuitry. Insome embodiments, input device 130 may be a hardware keyboard, a keypad,or a touch screen, through which a user may input information to system100. Display device 140 may include one or more display screens thatdisplay the simulation interface, result, or any related information tothe user.

Communication interface 150 may provide communication connections suchthat system 100 may exchange data with external devices. For example,system 100 may be connected to network 160. Network 160 may be a LAN orWAN that may include other systems S1 (172), S2 (174), and S3 (176).Systems S1, S2, and/or S3 may be identical to system 100, or may bedifferent systems. In some embodiments, one or more of systems innetwork 160 may form a distributed computing/simulation environment thatcollaboratively performs simulation task. In addition, network 160 maybe connected to Internet 180 to communicate with servers or clients thatreside remotely on the Internet.

FIG. 2A illustrates an exemplary network model. The term “network,” alsoknown as “electrical network,” refers to an interconnection ofelectrical elements such as resistors, inductors, capacitors,transmission lines, voltage sources, current sources, switches, etc. Anetwork may include one or more ports. A port may be a point at whichelectrical currents either enter or exit a network. The term “networkmodel” refers to a mathematical representation of a physical network. Anetwork model may include graphical representations of the network andassociated ports. A network model may also include a set of mathematicalexpressions and/or values that characterize the properties and/orbehaviors of the network. As used herein, a network model may also bereferred to as a network for simplicity.

Referring to FIG. 2, network 200 may include two ports: port 1 (202) andport 2 (204). In general, a network may include any number of ports. Foreach port, incident waves and reflected waves may be defined. Forexample, for port 1 (202), a₁ (212) represents incident waves and b₁(214) represents reflected waves. Similarly, for port 2 (204), a₂ (216)represents incident waves and b₂ (218) represents reflected waves. Theincident and reflected waves may be represented as voltage travellingwaves incident and reflected from a port normalized to a referenceimpedance Z₀ such that when squared the waves are equal to the powertraveling along the line connecting to the port. For example, for thenetwork 200 in FIG. 2, the incident and reflected waves on ports 1 and 2may be represented as:

$\begin{matrix}{{a_{1} = \frac{V_{i\; 1}}{\sqrt{Z_{01}}}};} & (1) \\{{b_{1} = \frac{V_{r\; 1}}{\sqrt{Z_{01\;}}}};} & (2) \\{{a_{2} = \frac{V_{i\; 2}}{\sqrt{Z_{02}}}};{and}} & (3) \\{b_{2} = {\frac{V_{r\; 2}}{\sqrt{Z_{02}}}.}} & (4)\end{matrix}$

In equations (1)-(4), V_(i1) and V_(i2) are voltage traveling wavesincident on ports 1 and 2, respectively. V_(r1) and V_(r2) are voltagetraveling waves reflected from ports 1 and 2, respectively. Z₀₁ and Z₀₂are reference impedances of ports 1 and 2, respectively. A set ofnetwork parameters may be expressed as:

$\begin{matrix}{\begin{pmatrix}b_{1} \\b_{2}\end{pmatrix} = {\begin{pmatrix}S_{11} & S_{12} \\S_{21} & S_{22}\end{pmatrix}{\begin{pmatrix}a_{1} \\a_{2}\end{pmatrix}.}}} & (5)\end{matrix}$

The network parameters defined by equation (5) are normally calledscattering parameters, or S-parameters. When expanded, equation (5)becomes:

b ₁ =S ₁₁ a ₁ +S ₁₂ a ₂ ; and   (6)

b ₂ =S ₂₁a₁ +S ₂₂ a ₂   (7)

The network parameters are therefore:

$\begin{matrix}{{S_{11} = \left. \frac{b_{1}}{a_{1}} \middle| \left( {a_{2} = 0} \right) \right.};} & (8) \\{{S_{21} = \left. \frac{b_{2}}{a_{1}} \middle| \left( {a_{2} = 0} \right) \right.};} & (9) \\{{S_{12} = \left. \frac{b_{1}}{a_{2}} \middle| \left( {a_{1} = 0} \right) \right.};{and}} & (10) \\{S_{22} = \left. \frac{b_{2}}{a_{2}} \middle| {\left( {a_{1} = 0} \right).} \right.} & (11)\end{matrix}$

If defining port 1 as an input port and port 2 as an output port, S₁₁may also be referred to as input reflection coefficient when port 2 ismatched terminated; S₂₁ may also be referred to as forward transmissioncoefficient when port 2 is matched terminated; S₁₂ may also be referredto as reverse transmission coefficient when port 1 is matchedterminated; and S₂₂ may also be referred to as output reflectioncoefficient when port 1 is matched terminated. As used herein, a port ismatched terminated when the port is connected to a load having animpedance equal to the characteristic impedance of the port, so that nowave is reflected from the load into the port. In general, either port 1or port 2 may be an input port.

When port 2 is connected to a load having an impedance equal to Z₀₂(also known as terminated in Z₀₂), no wave is reflected back into port2, therefore a₂=0. S₂₁ and S₁₁ can be related by the following equation:

$\begin{matrix}{{S_{21} = {\frac{\sqrt{Z_{01\;}}}{\sqrt{Z_{02}}} \times \frac{V_{out}}{V_{i\; n}}\left( {1 + S_{11}} \right)}},{where}} & (12) \\{{V_{i\; n} = {\sqrt{Z_{01}}\left( {a_{1} + b_{1}} \right)}},{and}} & (13) \\{V_{out} = {\sqrt{Z_{02}}{b_{2}.}}} & (14)\end{matrix}$

As used herein, a characteristic impedance refers to the physicalimpedance of a transmission line or waveguide. A reference impedancerefers to a port impedance to which network parameters can bereferenced. The reference impedance can be arbitrary and form the basisfor the network parameter calculations. For example, the definition ofS_(ij) implies that all ports except for port j are terminated in theirreference impedance and the source impedance of port j is equal to itsreference impedance.

Referring to FIG. 2B, network 200 is now connected to a voltage source224 at port 1 and a load 226 at port 2. Voltage source 224 has a voltageof V_(S) and a source impedance of Z_(S), which is represented byimpedance 222. Load 226 has a load impedance Z_(L). Further, thereference impedance of ports 1 and 2 are Z₀₁ and Z₀₂, respectively.Input impedance Z₁ at port 1 can be defined as the impedance across theterminals of port 1 when port 2 is terminated by load 226 while source224 along with source impedance 222 are disconnected. Similarly, outputimpedance Z2 at port 2 can be defined as the impedance across theterminals of port 2 with load 226 disconnected and source 224 replacedby a short circuit. In this case, source impedance 222 terminates port1. For the network model in FIG. 2B, the following coefficients can bederived.

Load reflection coefficient Γ_(L) can be represented by:

$\begin{matrix}{\Gamma_{L} = {\frac{Z_{L} - Z_{02}}{Z_{L} + Z_{02}}.}} & (15)\end{matrix}$

Source reflection coefficient Γ_(S) can be represented by:

$\begin{matrix}{\Gamma_{S} = {\frac{Z_{S} - Z_{01}}{Z_{S} + Z_{01}}.}} & (16)\end{matrix}$

Input reflection coefficient Γ₁ and output reflection coefficient Γ₂ canbe represented by:

$\begin{matrix}{{\Gamma_{1} = {\frac{Z_{1} - Z_{01}}{Z_{1} + Z_{01\;}} = \frac{b_{1}}{a_{1\;}}}},{and}} & (17) \\{\Gamma_{2} = {\frac{Z_{2} - Z_{02}}{Z_{2} + Z_{02}} = {\frac{b_{2}}{a_{2}}.}}} & (18)\end{matrix}$

Therefore, from equations (6), (7), and (15)-(18), input reflectioncoefficient Γ₁ and output reflection coefficient Γ₂ can be representedin terms of S-parameters as:

$\begin{matrix}{{\Gamma_{1} = {S_{11} + \frac{S_{12}S_{21}\Gamma_{L}}{1 - {S_{22}\Gamma_{L}}}}},{and}} & (19) \\{\Gamma_{2} = {S_{22} + {\frac{S_{21}S_{12}\Gamma_{S}}{1 - {S_{11}\Gamma_{S}}}.}}} & (20)\end{matrix}$

Therefore, if a matched load is used to terminate port 2 then Γ_(L)=0,and equation (19) becomes Γ₁=S₁₁. Similarly, if Z_(S)=Z₀₁ then port 1 ismatched and Γ_(S)=0, equation (20) becomes Γ₂=S₂₂.

As discussed above, the reference impedance in many RF and microwaveapplications is chosen to be 50 Ω. This is partly because thecharacteristic impedance of typical transmission line systems is around50 Ω. However, for systems involving power and ground lines, theeffective port input impedance is much smaller than 50 Ω. For example,the effective port input impedance in some power and ground systems maybe in the order of milliohms. In such cases, the network parameters,such as S-parameters, having a reference impedance of 50 Ω, may not besensitive to the variation of electrical properties of the power andground systems. For example, if the input impedance is about 5 mΩ, andthe reference impedance is 50 Ω, then the amplitude of S₁₁ would beabout 0.9998. When the input impedance changes to 10 mΩ, a 100%variation, the amplitude of S₁₁ would be about 0.9996, only a 0.02%variation.

FIGS. 3A and 3B illustrate an exemplary method for impedance adaptationfor a one-port network, in accordance with some disclosed embodiments.In FIG. 3A, a network model 300 is provided, with a network parameter S(S can be of matrix form that includes a plurality of values). In someembodiments, S can be a scattering parameter (or S-parameter). Fornetworks with more than one ports (e.g., M ports), S-parameters can beof a matrix form:

$\begin{bmatrix}S_{11} & S_{12} & \ldots & S_{1M} \\S_{21} & S_{22} & \ldots & S_{2M} \\\vdots & \vdots & \ddots & \vdots \\S_{M\; 1} & S_{M\; 2} & \ldots & S_{MM}\end{bmatrix}.$

Network model 300 may be a model of an electrical circuit. Network model300 may include a port 302, which is referred to as port 1. Networkparameter S is associated with port 1 and is defined based on referenceimpedance Z₀ of port 1. Network parameter S may include, for example, aparameter associated with the reflection coefficient Γ of port 1, suchas S₁₁. Reflection coefficient F is related to reference impedance Z₀and input impedance Z_(in) (304) of port 1 as follows:

$\begin{matrix}{\Gamma = \frac{Z_{\; {i\; n}} - Z_{0}}{Z_{i\; n} + Z_{0}}} & (21)\end{matrix}$

Therefore, input impedance Z_(in) can be computed by:

$\begin{matrix}{Z_{i\; n} = {Z_{0}\frac{1 + \Gamma}{1 - \Gamma}}} & (22)\end{matrix}$

It is noted that input impedance Z_(in) can be a function of frequency.For example, for different frequencies f_(i) and f_(j) in a frequencyrange of interest from f₁ to f₂ (f₁≦f_(i)≦f₂, f₁≦f_(j)≦f₂, f_(i)≠f_(j)),Z_(in)(f_(i)) can be different from Z_(in)(f_(j)). In this case, averageor weighted input impedance may be used. The average input impedance maybe calculated by averaging two or more impedance values within thefrequency range of interest. Additionally, weights can be added to oneor more impedance values to obtain a weighted average. Other methods mayalso be used to take into account input impedance values of the entireor a portion of the frequency range of interest. In any case, averageinput impedance can be obtained. For example, if input impedance in afrequency range of interest ranging from 1 to 15 mΩ the average inputimpedance of 10 mΩ may be obtained, after the process of averaging orweighted averaging, as discussed above. For simplicity, in the followingdescription, Z_(in) will represent average input impedance (or simply“input impedance”) instead of frequency-dependent input impedance,unless otherwise noted.

Referring now to FIG. 3B, new reference impedance Z_(0N) can be definedfor port 1 based on the computed input impedance Z_(in). In someembodiments, Z_(0N) can simply be equal to Z_(in). In other embodiments,Z_(0N) can be defined to be a value that is in the same or similar orderof Z_(in). For example, in typical RF and microwave applications, Z₀ maybe 50 Ω. If power and/or ground line is present in the circuit, Z_(in)may range from 1 to 100 ma By way of example, if Z_(in) is 15 mΩ, Z_(0N)can be defined to be 15 mΩ or other suitable values in the same orsimilar order of Z_(in). In this way, the reference impedance can beadaptively changed to suit for input impedance of a particular port.

After Z_(0N) is defined, a new network parameter S_(N) can be calculatedbased on Z_(0N). For example, S_(N) can be obtained as follows:

Z=(I−S)⁻¹(I+S)Z ₀   (23)

S _(N)=(Z−Z _(0N) I)(Z+Z _(0N) I)⁻¹   (24)

where Z is an impedance matrix and I is a unit matrix. Equations (23)and (24) are applicable to both one-port and multi-port networks.

FIGS. 4A and 4B illustrate an exemplary method for impedance adaptationfor a multi-port network, in accordance with some disclosed embodiments.In FIG. 4A, a network model 400 is provided. Network model 400 includesa plurality of ports: ports 1 (402), 2 (404), 3 (406), . . . M (408).Network parameter S (may be in matrix faun that includes a plurality ofvalues) is defined based on ports 1 to M. Each value in S may beassociated with at least one port and is defined based on the referenceimpedance of the port. For example, Z₀₁, Z₀₂, Z₀₃, . . . , Z_(0M) arethe reference impedance of ports 1, 2, 3, . . . M, respectively. Duringimpedance adaptation, input impedance of each port can be computed.

In one embodiment, input impedance of each port of network model 400 canbe computed iteratively. For example, input impedance Z_(in,1) (412) ofport 1 (402) can be computed based on S (e.g., S₁₁) and Z₀₁, accordingto, for example, equation (22), with all the other ports terminated bytheir respective reference impedance Z₀₂, Z₀₃, etc. Similarly, inputimpedance Z_(in,2) (414) of port 2 (404) can be computed based on S(e.g., S₂₂) and Z₀₂, with all the other ports terminated by theirrespective reference impedance Z₀₁, Z₀₃, etc. Similar computation can beperformed to obtain other input impedance: Z_(in,3) (416) of port 3(406) to Z_(in,M) (418) of port M (408).

Referring now to FIG. 4B, a new reference impedance may be defined foreach port of network model 400. For example, new reference impedanceZ_(01N) can be defined for port 1 (402) based on Z_(in,1) (412).Similarly, new reference impedance Z_(02N) can be defined for port 2(406) based on Z_(in,2) (414); new reference impedance Z_(03N) can bedefined for port 3 (406) based on Z_(in,3) (416); . . . new referenceimpedance Z_(0MN) can be defined for port M (408) based on Z_(in,M)(418). After all new reference impedance values have been obtained, aniteration cycle can be deemed complete.

Additional iteration cycles can be performed to further improve theaccuracy of the input impedance. For example, after a set of newreference impedance values have bee obtained, the new referenceimpedance (e.g., Z_(01N), Z_(02N), Z_(03N), . . . , Z_(0MN)) can replacethe respective original reference impedance (e.g., Z₀₁, Z₀₂, Z₀₃, . . .Z_(0M)). Thereafter, an updated input impedance (e.g., Z_(in,1)) can becomputed based on S (e.g., S₁₁) and its corresponding new referenceimpedance (e.g., Z_(01N)), with all other ports terminated by theirrespective new reference impedance. Accordingly, a set of updated inputimpedance can be obtained and the set of new reference impedance can besubsequently updated base on the updated input impedance. Such iterationcycles may be performed multiple times until a predetermined number ofcycles are reached or a predetermined tolerance is reached (e.g., belowa predetermined threshold). The tolerance/threshold may be defined basedon, for example, the difference between corresponding input impedancevalues between consecutive iteration cycles.

In another embodiment, the new reference impedance can be used toreplace old reference impedance on the fly. For example, in the firstiteration cycle, after Z_(in,1) of port 1 is obtained, new referenceimpedance Z_(01N) can be immediately defined based on and replaceoriginal reference impedance Z₀₁. As a result, during the computation ofZ_(in,2), port 1 can be terminated by Z_(01N), instead of Z₀₁, and allother ports are terminated by their respective original referenceimpedance. Similarly, after Z_(in,2) is obtained, Z_(02N) can beimmediately defined based on Z_(in,2) and replace original referenceimpedance Z₀₂. Thereafter, Z_(in,3) can be computed with port 1terminated by Z_(01N), port 2 terminated by Z_(02N), and all other portsterminated by their respective original reference impedance. In thisway, the new reference impedance replaces old reference impedance assoon as it has been defined based on available input impedance. Thistechnique may increase the convergence speed during iteration.

In yet another embodiment, input impedance may be computed withoutiteration. Referring to FIG. 4A, network parameter S (e.g.,S-parameters) may be equivalently represented by other types of networkparameter, such as impedance parameters (Z-parameters):

$\quad\begin{bmatrix}Z_{11} & Z_{12} & \ldots & Z_{1M} \\Z_{21} & Z_{22} & \ldots & Z_{2M} \\\vdots & \vdots & \ddots & \vdots \\Z_{M\; 1} & Z_{M\; 2} & \ldots & Z_{MM}\end{bmatrix}$

or admittance parameters (Y-parameters):

$\quad{\begin{bmatrix}Y_{11} & Y_{12} & \ldots & Y_{1M} \\Y_{21} & Y_{22} & \ldots & Y_{2M} \\\vdots & \vdots & \ddots & \vdots \\Y_{M\; 1} & Y_{M\; 2} & \ldots & Y_{MM}\end{bmatrix}.}$

Specifically, the diagonal elements Z_(ii) (i=1 . . . M) of theZ-parameter matrix can be obtained by measuring/calculating inputimpedance of port i while all other ports are open circuits. Similarly,the diagonal elements Y_(ii) (i=1 . . . M) of the Y-parameter matrix canbe obtained by measuring/calculating input admittance of port i whileall other ports are short circuits. Thereafter, the input impedanceZ_(in,i) (i=1 . . . M) can be obtained by:

$\begin{matrix}{Z_{{i\; n},i} = {\sqrt{\frac{Z_{ii}}{Y_{ii}}}.}} & (25)\end{matrix}$

As discussed above, Z_(in,i) can be a function of frequency and it isused herein as an average value over a frequency range of interest.After Z_(in,i) is obtained, new reference impedance Z_(0iN) can bedefined based on Z_(in,i) in a similar manner to the one discussedabove.

After new reference impedance values are defined, a new set of networkparameters S_(N) (e.g., in matrix form) may be calculated based on thenew reference impedance Z_(01N), Z_(02N), Z_(03N), . . . Z_(0MN) (e.g.,using equations (23) and (24)).

FIG. 5A shows a flow chart of an exemplary method for impedanceadaptation. In FIG. 5A, method 500 may include a series of steps, inaccordance with some embodiments. In step 502, there may be provided anetwork model with one or more ports (e.g., network 300 with port 302and network model 400 with ports 402, 404, 406, and 408). The networkmodel may include at least one network parameter (e.g., networkparameter S in FIGS. 3A and 3B) defined based on a reference impedance(e.g., reference impedance Z₀ in FIG. 3A). In step 504, the inputimpedance (e.g., input impedance Z_(in) in FIG. 3A) of at least one ofthe ports may be computed. In step 506, a new reference impedance (e.g.,reference impedance Z_(0N) in FIG. 3B) may be defined based on thecomputed input impedance. In step 508, a new network parameter (e.g.,network parameter S_(N)) may be calculated based on the new referenceimpedance. The dashed arrows above step 502 and below step 508 indicatethat the method 500 may be part of another method that includes moresteps.

FIG. 5B shows an exemplary method of implementing step 504 in FIG. 5A.As shown in FIG. 5B, step 504 may include a sub step 5040, in which animpedance value (e.g., Z_(ii)) may be computed based on the networkparameter. In sub step 5042, an admittance value (e.g., Y_(ii)) may becomputed based on the network parameter. In sub step 5044, the inputimpedance can be computed based on the impedance and admittance values(e.g., equation 25).

FIG. 5C shows another exemplary method of implementing step 504 in FIG.5A. As shown in FIG. 5C, step 504 may be implemented in an iterativemanner. In sub step 5046, the input impedance may be computed based onthe network parameter and reference impedance of the corresponding port.In sub step 5047, a difference of input impedance obtained fromconsecutive iterations can be computed. For example, the difference canbe an absolute value of input impedance difference of a particular portbetween consecutive iteration cycles, or an average of input impedancedifferences of a plurality of ports between consecutive iterationcycles, or any other suitable measures. In sub step 5048, the differenceis compared with a predetermined threshold. If the difference is belowthe threshold (branch YES), the method proceeds to step 506 in FIG. 5A.If the difference is not below the threshold (branch NO), the methodproceeds to sub step 5049, where the reference impedance is updatedbased on corresponding input impedance computed in sub step 5046, andreturns to sub step 5046 to compute new input impedance based on thenetwork parameter and the updated reference impedance.

In electromagnetic simulation, network parameters, such as S-parameters,can be directly input and utilized by simulation software, such asSPICE-like circuit simulators. Direct S-parameter simulation maygenerally require relatively longer simulation time, and may suffer fromdivergence issue in time domain due to its passivity violation.Alternatively, S-parameters can be converted into equivalent circuitmodel first using macro-modeling method, such as rational functionfitting method, and then be inserted into simulation software. Withmacro-modeling techniques, the network model characterized byS-parameters may be approximated by rational functions throughvector-fitting. Passivity enforcement may be applied is necessary. Thenetwork model may then be converted into equivalent circuit model forsimulation and analysis. Such equivalent circuit model may achievefaster simulation speed than simulating directly with S-parameters.

The above-disclosed impedance adaptation method and system may beapplied during equivalent circuit modeling process. As discussed above,in applications evolving power and/or ground systems, the commonly used50 Ω reference impedance may not achieve high accuracy in rationalfunction fitting because the S-parameters are insensitive to electricalproperty variations of power/ground systems. Therefore, the resultingequivalent circuits may suffer poor accuracy. With the disclosed methodand system, the reference impedance of each port is automaticallyadapted based on input impedance. Therefore, the resulting networkparameters may be much more sensitive to the electrical propertyvariation of power/ground systems, thereby improving accuracy of theequivalent circuit model.

FIG. 6 is a flow chart of an exemplary method of modeling electricalcircuit using new network parameters resulting from impedanceadaptation, in accordance with some disclosed embodiments. In FIG. 6,method 600 may include a series of steps. Step 602 includes performingrational function fitting based on network parameters. The networkparameter may be the new network parameter after impedance adaptation.In Step 604, equivalent circuit model may be generated based on therational function fitting results. The equivalent circuit model may bean approximation of the network model (e.g., network model 200, 300, or400) characterized by network parameters. During simulation, theequivalent circuit model may be analyzed by SPICE-like circuit simulatorto simulate electrical property and/or behavior of the network model. Asindicated by the dashed arrows above step 602 and below step 604, method600 may be part of another method that includes more steps. Method 600may also be joined to method 500. For example, step 508 may be followedby step 602.

S-parameters are often used in applications involving high frequencies,such as frequencies in RF and microwave ranges, because they arerelatively easier to measure the other types of network parameters. Themethod and system disclosed herein can be applicable to referenceimpedance adaptation in the context of S-parameters, regardless ofwhether the S-parameters are obtained from computation or measurement.

FIG. 7 shows an exemplary graph comparing S-parameter variations beforeand after performing reference impedance adaptation, in accordance withsome disclosed embodiments. In FIG. 7, the dashed-line curve representsthe amplitude of an S-parameter in a frequency range of interest (0-5000MHz) before reference impedance adaptation, while the solid-line curverepresents the amplitude of the S-parameter after reference impedanceadaptation. It can be seen that before the reference impedanceadaptation, the amplitude values (normalized) concentrate toward 1, withvery little variations. In contrast, the curve after reference impedanceadaptation exhibits large variations. Therefore, the reference impedanceadaptation may increase the sensibility of S-parameters.

A simulation project may include one or more network models. For eachmodel, similar process may be preformed to adaptively change thereference impedance and generate new network parameters.

In the foregoing Description of Exemplary Embodiments, various featuresare grouped together in a single embodiment for purposes of streamliningthe disclosure. This method of disclosure is not to be interpreted asreflecting an intention that the claims require more features than areexpressly recited in each claim. Rather, as the following claimsreflect, inventive aspects lie in less than all features of a singleforegoing disclosed embodiment. Thus, the following claims are herebyincorporated into this Description of the Exemplary Embodiments, witheach claim standing on its own as a separate embodiment of theinvention.

Moreover, it will be apparent to those skilled in the art fromconsideration of the specification and practice of the presentdisclosure that various modifications and variations can be made to thedisclosed systems and methods without departing from the scope of thedisclosure, as claimed. Thus, it is intended that the specification andexamples be considered as exemplary only, with a true scope of thepresent disclosure being indicated by the following claims and theirequivalents.

What is claimed is:
 1. A method, implemented by a computer, foranalyzing electrical properties of a circuit, the method comprising:providing a network model of the circuit having at least one port,wherein the network model includes at least one network parameter, thenetwork parameter being associated with the port and being defined basedon a reference impedance of the port; computing, by the computer, aninput impedance of the port based on the network parameter; defining anew reference impedance for the port based on the input impedance; andcalculating, by the computer, a new network parameter of the networkmodel based on the new reference impedance.
 2. The method of claim 1,the computing the input impedance comprising: computing an impedancevalue associated with the port based on the network parameter; computingan admittance value associated with the port based on the networkparameter; and computing the input impedance of the port based on theimpedance and admittance values.
 3. The method of claim 1, wherein thereference impedance is 50 ohms.
 4. The method of claim 1, wherein thedefining the new reference impedance includes: defining the newreference impedance to be the same as or in a similar order of thecomputed input impedance.
 5. The method of claim 1, wherein: the networkmodel includes a plurality of ports and a plurality of networkparameters, each of the plurality of network parameters being associatedwith at least one port of the plurality and being defined based on thereference impedance; the step of computing input impedance includescomputing a corresponding input impedance for each of the plurality ofports based on at least one of the network parameters; the step ofdefining new reference impedance includes defining a correspondingreference impedance for each of the plurality of ports based on thecorresponding input impedance of the port; and the step of calculatingincludes calculating a corresponding new network parameter for each ofthe plurality of network parameters based on the defined referenceimpedance for each of the plurality of ports.
 6. The method of claim 5,wherein the step of computing input impedance further includes:computing the corresponding input impedance for each of the plurality ofports iteratively until a difference of the corresponding inputimpedance between consecutive iterations is below a predeterminedthreshold.
 7. The method of claim 1, further comprising: performing, bythe computer, rational function fitting based on the new networkparameter; and generating an equivalent circuit model of the networkmodel based on the rational function fitting result.
 8. The method ofclaim 1, where in the circuit is a microwave or radio frequency (RF)circuit.
 9. A non-transitory computer-readable medium encoded withsoftware code instructions, when executed by a computer, implementing amethod for analyzing electrical properties of a circuit, the methodcomprising: providing a network model of the circuit having at least oneport, wherein the network model includes at least one network parameter,the network parameter being associated with the port and being definedbased on a reference impedance of the port; computing, by the computer,an input impedance of the port based on the network parameter; defininga new reference impedance for the port based on the input impedance; andcalculating, by the computer, a new network parameter of the networkmodel based on the new reference impedance.
 10. The non-transitorycomputer-readable medium of claim 9, the method comprising: computing animpedance value associated with the port based on the network parameter;computing an admittance value associated with the port based on thenetwork parameter; and computing the input impedance of the port basedon the impedance and admittance values.
 11. The non-transitorycomputer-readable medium of claim 9, wherein the reference impedance is50 ohms.
 12. The non-transitory computer-readable medium of claim 9,wherein the defining the new reference impedance includes: defining thenew reference impedance to be the same as or in a similar order of thecomputed input impedance.
 13. The non-transitory computer-readablemedium of claim 9, wherein: the network model includes a plurality ofports and a plurality of network parameters, each of the plurality ofnetwork parameters being associated with at least one port of theplurality and being defined based on the reference impedance; the stepof computing input impedance includes computing a corresponding inputimpedance for each of the plurality of ports based on at least one ofthe network parameters; the step of defining new reference impedanceincludes defining a corresponding reference impedance for each of theplurality of ports based on the corresponding input impedance of theport; and the step of calculating includes calculating a correspondingnew network parameter for each of the plurality of network parametersbased on the defined reference impedance for each of the plurality ofports.
 14. The non-transitory computer-readable medium of claim 13,wherein the step of computing input impedance further includes:computing the corresponding input impedance for each of the plurality ofports iteratively until a difference of the corresponding inputimpedance between consecutive iterations is below a predeterminedthreshold.
 15. The non-transitory computer-readable medium of claim 9,the method further comprising: performing rational function fittingbased on the new network parameter; and generating an equivalent circuitmodel of the network model based on the rational function fittingresult.
 16. The non-transitory computer-readable medium of claim 9,where in the circuit is a microwave or radio frequency (RF) circuit. 17.A system for simulating electrical properties of a circuit, comprising:a processor; and a memory communicatively coupled to the processor,wherein the processor is configured to: load a network model of thecircuit into the memory, wherein the network model includes at least oneport and at least one network parameter, the network parameter beingassociated with the port and being defined based on a referenceimpedance of the port; compute an input impedance of the port based onthe network parameter; obtain a new reference impedance for the portbased on the input impedance; and calculate a new network parameter ofthe network model based on the new reference impedance.
 18. The systemof claim 17, the processor is configured to: compute an impedance valueassociated with the port based on the network parameter; compute anadmittance value associated with the port based on the networkparameter; and compute the input impedance of the port based on theimpedance and admittance values.
 19. The system of claim 17, wherein thereference impedance is 50 ohms.
 20. The system of claim 17, where in thecircuit is a microwave or radio frequency (RF) circuit.